Everything that appears to be designed has a designer.
The universe appears to have been designed.
Therefore, the universe has a designer.
This is essentially the argument from design (as I've understood it), and it is a rock-solid argument if the premises are true. So, are they?
We'll assume that by "designer" we mean an intelligent being capable of forming matter in ways that the matter cannot form itself (even if under the influence of some mechanical laws), and "appearance of design" to be these forms. We can call these forms properties. If we manage to clearly define these properties (which is work yet ahead of us), then premise 1 is true. Otherwise we can always question whether it's true that a designer must be responsible for any appearance of design, destroying the argument.
But these properties must also be defined so that they fit the object in premise 2. We're essentially using an analogy, where we compare an object for which we don't initially know there is a designer, with objects we do know have a designer. But the latter objects exist within the first object, as do their designers. In reality, we have no idea under what circumstances the universe itself exists. If the universe exists in a space-time much like the space-time within the universe, then yes, we can directly compare the universe with objects within the universe, but that leads to infinite regress. What environment does the universe that holds the universe exist in? And what environment does the universe that holds the universe that holds our universe exist in? (Also, I would think we should be able to detect at least one universe within our own, if this babushka doll structure was a fact.)
Sooner or later you're going to have to posit a very different environment from what we find inside the universe, and at that point the analogy breaks down. For what is true for objects in one environment, is not necessarily (almost certainly not) true for objects in a different environment. In this case it's even more true, since forming existing matter into designed objects within the universe is very different from creating the universe itself.
So, the argument fails because of its premises.
Premise 1: Everything that appears to be designed has a designer.
This is only true if we can identify properties of design that requires a designer, and can confirm that all objects that appears to be designed has these properties.
Premise 2: The universe appears to have been designed.
If the universe appears to have been designed from our perspective, it is only because we're comparing its inside with objects on its inside. We have no idea what reality the universe itself exists in, so we have no idea if the properties we define in premise 1 holds true for the universe as well. But Christian theology assumes that what exists outside the universe is a nothingness with an uncaused, timeless, immaterial, powerful and intelligent mind in it. This is a very different environment from the one inside the universe, so if this is true, we cannot use the design argument to demonstrate the existence of said being by implying this universe must have been designed as designed objects in it are designed. We would need an entirely different standard of design that applies equally well to both environments.
Conclusion: Therefore, the universe may possibly, maybe, perhaps have a designer, or not.
That's the proper conclusion for now, me thinks.